- #1

NanaToru

- 24

- 0

## Homework Statement

A bacteria culture initially contanis 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420.

a. Find an expression for the number of bacteria after t hours.

b. find the number of bacteria after 3 hours

c. find the rate of growth after 3 hours.

d. when will population reach 10,000?

b. find the number of bacteria after 3 hours

c. find the rate of growth after 3 hours.

d. when will population reach 10,000?

## Homework Equations

This is done in section of the book of expontial growth and decay, so equations

dP/dt = kP

P(t) = P0 e^kt

## The Attempt at a Solution

I [/B]I managed to solve it, but I had some questions about the exponentials.

For part a, I got

P'(t) = 100P, and if P'(1) = 420, P = 4.2

However, for c., I had to end up taking the differential of P(t) to get P'(t) = 143.5e^1.435t

Ultimately, at t = 1, these give the same answer. But I don't understand how I'm supposed to know when to get either equation... Would my answer for C have been incorrect for A?